In this paper, relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered. By introducing almost surely D–α-contracting property for random dynamical systems, we obtain a global random attractor of the stochastic wave equation νutt + ut − uν + f (uν) = √ νẆ endowed with Dirichlet boundary condition for any 0 < ν 1. The upper semicontinuity of thi...

The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that this chaotic behaviour still appears when ...